The amount of data collected from spaceborne remote sensing has substantially increased in the last years. During same time period, the ability to store or transmit data has not increased as quickly. At this time, there is a growing interest in developing compression schemes that could provide both higher compression ratios and lower encoding/decoding errors. In the case of the spaceborne Synthetic Aperture Radar (SAR) earth observation system developed by the French Space Agency (CNES), the volume of data to be processed will exceed both the on-board storage capacities and the telecommunication link. The objective of this paper is twofold: to present various compression schemes adapted to SAR data; and to define a set of evaluation criteria and compare the algorithms on SAR data. In this paper, we review two classical methods of SAR data compression and propose novel approaches based on Fourier Transforms and spectrum coding.